Given a general graph on a plane, deform the plane in 3 space

[Integral]

I just got a call from a good friend who is in the final terms of his ME degree. He needed some leads on the field of math that was needed to determine a solution to this problem.

Given a general graph on a plane, deform the plane in 3 space, now what is the equation which describes the graph.

I told him differential geometry.

Did I do right?

(I told him he should come in here and post his question, this is just in case he doesn't!

 

[lethe]

Originally posted by Integral

I told him differential geometry.

Did I do right?

yeah, i would say. or perhaps differential topology.

i have never seen this particular problem, but my differential topology class dealt with intersection theory, which uses deformations one of its tools.

 

[Integral]

Ok, thanks.
I did mention topology to him also.

He was a bit disapointed, he was hopeing for a quick foumula, not an introduction to an intire field!

 

[lethe]

Originally posted by Integral
Ok, thanks.
I did mention topology to him also.

He was a bit disapointed, he was hopeing for a quick foumula, not an introduction to an intire field!

well, i don t know exactly what he wants to do, but if the problem is very specific, it may have a very specific solution, in which case, you won t need to learn a whole field.

perhaps i am not understanding the problem correctly, but to me, what you are asking sounds trivial.

if i have a graph of v=f(u) in the plane, and i want to embed this plane in R3 with embedding (x(u,v),y(u,v),z(u,v)) then the resulting curve will have a graph given by (x(u,v(u)),y(u,v(u)),z(u,v(u)). this holds no matter what the shape of the embedding is, so if you know what you want for your deformation, then you are in business.

this seems trivial to me, so i assume i am misunderstanding the problem. but the point is, it may well be that he doesn t need to learn the whole body of differential geometry/differential topology. we can t say until we know what the question is.

is he going to post it here?

 

[matt grime]

Originally posted by Integral
I just got a call from a good friend who is in the final terms of his ME degree. He needed some leads on the field of math that was needed to determine a solution to this problem.

Given a general graph on a plane, deform the plane in 3 space, now what is the equation which describes the graph.

I told him differential geometry.

Did I do right?

(I told him he should come in here and post his question, this is just in case he doesn't!

Why on Earth would you need any differential geometry for this problem?

Perhaps you should try and get him to explain what he means by deforming the plane. Basic manipulation of formulae should give you the answer

 

[Integral]

I was hoping that he would come in here and post more information.

Guess not.

Thanks for the input I will pass it along next time I see him.